Calculus BC Integrals HELP ASAP!

Question

Use geometry to evaluate  for  

Answer 1

Joy

The integral will be the area between the function and the x-axis.

For x = 0 to 5, f(x) = 5 , so this area will be 5 x 5 = 25

for 5<x<10, f(x) = 10 - x. When x = 5, f(x) = 5. When x = 10, x = 0.

So this area is area of a right triangle, base 10-5 = 5, height 5. So the area is 5 x 5 / 2 = 12.5

So to find the integral add the two areas together, 25 + 12.5 = 37.5 square units

Mike